4.1 Investigate and approximate the area of polygons  (Page 3/3)

6.2 Add all the numbers from 1 to 20 inclusive. Look for a pattern and a short way. Write down what you did and your answer on the dotted line below. Then check your answer the long way. You may use a calculator to do so.

7. Another interesting pattern can be seen in the answers if you add:

• 1 to 10 inclusive = _____
• 11 to 20 inclusive = _____
• 21 to 30 inclusive = _____
• 31 to 40 inclusive = _____
• 41 to 50 inclusive, and so on to 100. Write down the answers, study them and try to explain why this pattern occurs.

8. More patterns with shapes. The following pattern may be made with toothpicks, one for each straight line.

• Pattern: Each time we add one triangle, we need ______more toothpicks.
• We could put our information into a table. Please complete it.

• How are the last two answers calculated? There are at least two different ways (without a calculator) and it is important that you should discuss these with your friends.

Hint: Maybe you could look at the toothpicks needed for six triangles and use them to calculate how many toothpicks are needed for 17 triangles, or you could think that you know the general pattern and just apply it to find out how many toothpicks are needed for 17 triangles. Your discussion is important, so the answers are not being given to you.The same applies to the 25 triangles.

8.4 Write down how you calculated the answers for

1. 17 triangles
2. 25 triangles

9. Complete the table:

TEST YOUR PROGRESS

1. Do the following show tessellation? Write “yes” or “no” for each one.

Using the trapezium and diamond ________

Using just the trapezium ________

Using circles _______

2. Write down one way in which the sides of a trapezium differ from the sides of a

parallelogram .

3. Why is the triangle used in the building of the framework of the roofs of houses?

4. On a floor there are 10 tiles in a row and there are 17 rows of tiles. How many tiles are there altogether?

5. Dad uses 135 tiles to tile a stoep. He places 9 tiles across the width of the stoep. How many tiles are there in the length of the stoep?

6. Make a diagram to show what a square tiled area would look like if 16 square tiles were used to cover it. Use your ruler to draw in the tiles.

7. Complete the table:

8. Complete this table:

9. Thirty squares are made with toothpicks as shown in the diagram (one toothpick for each straight line). How many toothpicks are needed?

1. Find a pattern and write down the missing numbers: 5; 13; 21; 29; ___;___

Assessment

Memorandum

ACTIVITY 1area of polygons

1.1 to 1.3 Practical own work and recording of it.

2. 4 whole blocks and 5 and a bit blocks = about 9 blocks

3.1 6

3.2 12

• about 8 square cm
• 7 square cm

• counted the length on the long side and the number of tiles on the short side.
• 5 x 2 = 10 tiles or 10 square cm

• Drawing
• 4m x 3m = 12 square metres
• Drawing

• 6 rows
• Drawing

8.1 Yes

8.2 Drawing

9. 23 x ? =736

32 tiles

10. 75 x 54 = 4 050 tiles!

ACTIVITY 2 Patterns

1.4

4 shapes

2. Multiples of 9 – the digits forming each multiple of 9 add up to 9, so 54 is a multiple of 9; 72 is a multiple of 9. This is useful for checking answers.

• Missing output numbers: 35; 42; 49; 70; 91
• Flow diagram: input numbers: 1; 2; 3; 4; 5; 6; 7; 8; 9; 10 Operator: x 7

Output numbers: 7; 14; 21; 28; 35; 42; 49; 56; 63; 70

• multiplied by 7

4.1

4.2 Flow diagram:

Input numbers: 1; 2; 3; 4; 7; 8; 9; 10; 20; 50

Operators: x 5 + 2

Output numbers: 7; 12; 17; 22; 37; 42; 47; 52; 102; 252

4.3 multiplied by 5 and 2 was added to the answer.

5.1

5.2 multiplied by 2 and 1 was added to the answer

5.3

5.3 multiplied by 4 and 1 was subtracted from the answer.

• It can! x 4 – 1

• Own

6.2 1 + 20; 2 + 19; 3 + 18; 4 + 17; 5 + 16; 6 + 15; 7 + 14; 8 + 13; 9 + 12; 10 + 11

10 x 21 = 210

7. 55; 155; 255; 355; 455 etc.

Own

8.1 2

8.2

• Discussion

8.4 (a) 17 x 2 + 1

(b) 25 x 2 + 1

9.

Test your progress

1.1 Yes

1.2 Yes

1.3 No

2. Only 1 pair of opposite sides are parallel; they are not equal in length.

3. It is a rigid shape.

4. 170 tiles

5. 15 tiles

6. Diagram 4 by 4

7.

8.

10. 5; 13; 21; 29; 37; 45